Finite Group Databasebeta

C2×#13112714 #15752902

order3328
automorphism?
homologyAbelianization (H1) = C2×C42 · Schur multiplier (H2) = C25

Aliases

direct productC2×#13112714

Splittings

SylowC13 ⋊ C2×#1294

Subgroups

subgroupG/H
centerC24C22⋊Dic13
commutatorC2×C4×C13C2×C42
FrattiniC23×C4C22×D13
FittingC2×C13×#380C2
socleC24×C13C22⋊C4
prime radicalC25×C13D4
cosocleC23×C4×C13C23
hypercenterC2×#380D13
hypocenterC13C2×#1294
LCSG ▷ C2×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C24 ◁ C24×C4 ◁ C2×#380

1454 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 832

Conjugacy classes & character table

412 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 59551);